New insight into the effects of Ca(II) on cake layer structure in submerged membrane bioreactors

<div><p>The effects of Ca(II) on the structure of the cake layer in submerged membrane bioreactors (SMBRs) were investigated in this study. Three parallel laboratory-scale SMBRs were operated with synthetic municipal wastewater with three Ca(II) levels (82, 208 and 410 mg l⁻¹). As the Ca(II) concentration increased, the sludge floc size increased and the molecular weight of the soluble microbial products (SMP) in the bulk liquid decreased. These observations were attributed to the neutralization and bridging function of Ca(II). Furthermore, Ca(II) addition did not change the thickness of the cake layer, but inhibited the deposition of other elements, such as Al, Si, Mg, and Fe. As a result of Ca(II) addition, the cake layer became less compact and more porous. The interspaces among the flocs in the cake layer helped to reduce the membrane fouling potential.</p></div

Classification accuracy for various neuroimaging markers (50% of the data are used as training set and the rest 50% as test set, except for the last column, where a leave-one-out cross-validation is used).

<p>The best results are achieved when we combine the features from the community matrix <i>K</i> and the asymmetry measure <i>ρ</i>. The accuracy of classification using SVM versus the number of edges selected from the community matrix <i>K</i> can be found in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036733#pone.0036733.s007" target="_blank">Text S4</a>.</p

Illustration of two asymmetry measures using a pair of equavelent regions A and A’ for demonstration. a global connectvity asymmetry measure <i>ρ.</i>

<p>The connectivity profile of A (i.e., vetor [<i>K</i>(A,A’), <i>K</i>(A,B’), <i>K</i>(A,B)]) and A’ (vector [i.e., <i>K</i>(A’,A), <i>K</i>(A’,B), <i>K</i>(A’,B’]) are represented by dashed lines of bule and green, respectively. Note that the connectivity <i>K</i>(A,A’) equals <i>K</i>(A’,A), and are both ploted for clarity. <b>b</b> pairwise brain-region synchronization <i>d</i>, which is the standardized Euclidean distance between BOLD signals from equavalent brain regions A and A’, B and B’, respectively (by black dashed lines).</p

Visualization of group difference in terms of community matrix <i>K</i>, b is an enlargement of a.

<p>The white pixels correspond to edges in <i>K</i> that are more discriminative across the two groups (these edges have a larger regression coefficient in sparse regression). Specifically, the second main diagonal (as is indicated by a yellow dashed line in <b>b</b>) contains connectivities between pairs of bilaterally homologous brain regions. In figure <b>b</b>, the connectivities between brain region 79 and 80 (left and right heschl), 87 and 88 (left and right temporal-pol-mid) are most significant. Here we highlight most of the discriminative edges in by 5 red boxes, which belong to frontal, limbic, occipital, parietal, and temporal lobe, respectively.</p

Visualization of Cross-Correlation matrix (a and b) versus Community matrix <i>K</i> (c and d) for the same healthy control (left column) and epileptic patient (right column).

<p>From <b>c</b> and <b>d</b> we can see that the pixels distributed near the main diagonal are much brighter in healthy subjects than those in patients, as are highlighted by the three boxes, which cannot be observed in cross-correlation matrix (<b>a</b> and <b>b</b>). These pixels mostly correspond to the functional connections across the two hemispheres.</p

Pairwise brain-region synchronization <i>d</i> for 45 pairs of equivalent brain regions a, Visualization of <i>d</i> for all subjects, with each row corresponding to every subject, and each column represents each pair of equivalent brain regions.

<p>The top 80 rows are healthy controls, and the bottom 100 rows are epileptic patients, separated by a black dashed line. A large <i>d</i> indicates weak synchronization between a pair of brain regions and thus a high level of asymmetry. <b>b</b>, The ratio between group mean value (<i>d_</i>P/<i>d_</i>H) for each pair of brain regions. The red line corresponds to <i>d_</i>P/<i>d_</i>H = 1, i.e., the two groups have the same group mean value. The most asymmetric brain regions according to <i>d_</i>P/<i>d_</i>H (i.e., hippocampus) is highlighted. <b>c</b>, The 10 most discriminative regions across the two groups according to P value of two sample t-test, with the mean and standard deviation of <i>d</i> being shown for the two groups. The corresponding <i>P</i> values are (unit: 10⁻³): 0.0000004, 0.0001, 0.0001, 0.0028, 0.0032, 0.0044, 0.0086, 0.0252, 0.0267, 0.1217. As is shown, <i>d</i> is much larger for epileptic patients than for healthy controls.</p